Question

line segment ts is tangent to circle o at point n. if the measure of ∠qnt is 74°, what is the measure of (overarc{qpn})?
37°
74°
148°
212°

Explanation:

Step1: Recall tangent-chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of its intercepted arc. For $\angle QNT$, it intercepts arc $\widehat{QN}$.

Step2: Calculate arc $\widehat{QN}$

$\text{Measure of } \widehat{QN} = 2 \times m\angle QNT$
$\text{Measure of } \widehat{QN} = 2 \times 74^\circ = 148^\circ$

Step3: Find total circle degree

A full circle is $360^\circ$.

Step4: Calculate arc $\widehat{QPN}$

$\text{Measure of } \widehat{QPN} = 360^\circ - \text{Measure of } \widehat{QN}$
$\text{Measure of } \widehat{QPN} = 360^\circ - 148^\circ = 212^\circ$

Answer:

212°